Orthomorphic permutations have good characteristics in cryptosystems. In this paper, by using of knowledge about relation between orthomorphic permutations and multi-output functions, and conceptions of the generalize...Orthomorphic permutations have good characteristics in cryptosystems. In this paper, by using of knowledge about relation between orthomorphic permutations and multi-output functions, and conceptions of the generalized Walsh spectrum of multi-output functions and the auto-correlation function of multi-output functions to investigate the Walsh spectral characteristics and the auto-correlation function characteristics of orthormophic permutations, several results are obtained.展开更多
We will give the definition of the linear kernel of boolean functions and prove that, by a reversible linear transformation, any linear structure boolean function can be transformed into a boolean function which is li...We will give the definition of the linear kernel of boolean functions and prove that, by a reversible linear transformation, any linear structure boolean function can be transformed into a boolean function which is linear to some variables, is non-relative to some variables and is of non-linear structure to other variables; any Partially-Bent Function can be transformed into a boolean function which is linear to some variables, is nonrelativeto some variables ans is bent to other variables. We will also discuss the Walsh Spectral Characterization of Partially-Bent Functions.展开更多
基金Supported by State Key Laboratory of InformationSecurity Opening Foundation(01-02) .
文摘Orthomorphic permutations have good characteristics in cryptosystems. In this paper, by using of knowledge about relation between orthomorphic permutations and multi-output functions, and conceptions of the generalized Walsh spectrum of multi-output functions and the auto-correlation function of multi-output functions to investigate the Walsh spectral characteristics and the auto-correlation function characteristics of orthormophic permutations, several results are obtained.
基金Supported by Prof. Y. Xu under his grant in program of"One Hundred DistinguishedChinese Scientists"of the Chinese Academy of Sciences, the National Natural Science Foundation of China (No.10371122) and Postgraduate Innovation Fund of Chinese Academy of Sciences
文摘We will give the definition of the linear kernel of boolean functions and prove that, by a reversible linear transformation, any linear structure boolean function can be transformed into a boolean function which is linear to some variables, is non-relative to some variables and is of non-linear structure to other variables; any Partially-Bent Function can be transformed into a boolean function which is linear to some variables, is nonrelativeto some variables ans is bent to other variables. We will also discuss the Walsh Spectral Characterization of Partially-Bent Functions.
